This study is a nation-wide cooperative group study investigating whether Cyclophosphamide or Taxol is more effective when added to Cisplatin chemotherapy or whether giving two cycles of a related drug, Carboplatin, followed by Taxol by vein and Cisplatin into the abdominal cavity is more effective in subjects with advanced ovarian cancer. Following the chemotherapy regimen (6 cycles), a second surgery (second look laparatomy) is recommended to determine if the cancer has been eliminated.